I think Advent's bad economy is simply a faction quirk. Rather than balance the Advent economy to approach the economies of the other races, I think what's supposed to be Advent's strength (namely, military) deserves a buff instead to make them competitive with other races.
Unfortunately, this causes some pretty significant distortions based on map size or start positions. The obvious case is an Advent in the pocket in a 5v5 multiplayer simply will never compete with a pocket TEC in multiplayer. If Advent had the strongest envoys in the same way they have the weakest economy then that could clear up the team-based issues, but this is not the case. Furthermore, it doesn't deal with the problem of more expansive 1v1 scenarios where there is lots of time to build a strong economy at the start of the game.
In any case, Advent needs more economic techs at the 4-7 lab levels. Resource Focus would be a great place to start; that tech has been useless since the day the game shipped (I'm given to understand it had a purpose in the beta, but its numbers are totally out of whack now), and Advent lacks a true refinery.